Spectral bounds on the chromatic and independence numbers
A Lean 4 / Mathlib formalization of classical eigenvalue bounds for a finite simple graph G on a nonempty vertex type, with λ_max and λ_min the largest and smallest eigenvalues of its real adjacency matrix: the average degree is at most λ_max and λ_max is at most the maximum degree (Collatz–Sinogowitz); G is (⌊λ_max⌋ + 1)-colourable (Wilf 1967); if G has an edge, every proper colouring uses at least 1 − λ_max/λ_min colours (Hoffman 1970); and if G is k-regular with k ≥ 1, every independent set has at most n(−λ_min)/(k − λ_min) vertices (Hoffman's ratio bound). Mathlib has the spectral…
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